1. The past

Before digital computers were developed, engineers wishing to
simulate physical processes employed analogue computers; and,
just at the end of the "analogue era" (approx 1955), one of these
was created
for the simulation of combustion processes [Reference 1].

It may be worth considering, because the concept led
naturally to the first digital-computer models.

The concept was this:-

The fluid-flow processes in combustion systems had been
(qualitatively) simulated [Reference 2, 1949]
by the use of "cold-flow" models using air or water, of the kind
which are still found useful at the present time ;
however, these
could not predict such processes as ignition and extinction.

These processes are the consequences of the facts that the rate of
a combustion reaction is:

negligible at low temperatures, because it varies as
exp(constant/T);

zero at the uppermost temperature because all the fuel has been consumed;

and finite at intermediate temperatures, but with a bias towards the higher
ones;

Therefore a "combustion analogue" could be an air- or water-flow
system which embodied an array of heaters and thermocouples which
were so linked that the heat input depended on the local
temperature in a manner similar to that which characterises
combustion.

Such an
apparatus
was created, by the present author; the
heater/thermocouple pairs were arrayed on a two-dimensional
cartesian grid; and the relation between the heat input and the
local temperature was contrived by manual adjustment.

The phenomenon of the extinction of baffle-stabilised flame was
indeed predicted; and it could be truly claimed that agreement
between the predictions and actual combustion experiments was as
satisfactory as could be expected, in view of the crudeness of the
rate-versus-temperature expression, and of the fact that the
density variations which are present in real combustion chambers
were not simulated.

The studies were not confined to uniform-composition gases, but
extended also to flows in which the fuel and oxidant entered in
separate streams.

Re-reading Reference 1 for the first time in more than forty years,
the present author is impressed by:-

the understanding which it exhibits of the essence of the
combustion process, evidently a consequence of the need to
participate in the heating-rate-versus-temperature interaction;

its acceptance of the necessity for discretization;

its total unawareness of the turbulence-chemistry-interaction
problem; and

its naive hopefulness.

It may be interesting to remark that:

the author did present the concept to Rolls Royce Ltd, for use in
its gas-turbine-combustor-development program;

it was sympathetically considered by the then head of combustion
research, Stephen Bragg; but

it was not adopted.

In some respects, the combustion-analogue proposal was too far in
advance of its time. Thus Stephen Bragg himself had just (1956) published
a much-acclaimed paper [Reference 3] on a zero-dimensional
model of the extinction of flames; whereas the analogue was already
two-dimensional, and was capable of being extended to three
dimensions.

However, it was also behind the times; for the digital computer was
already beginning to be used for simulating simple combustion processes
[Reference 4]; and before long even the present author, whose first
(approx 1954)
numerical computations had been performed by graphical means
[Reference 5], had
"gone digital" [Reference 6].

The graphical method, it might be remarked, was very educative; for its
user could feel as though he were a part of the flame-development
process, which, in a sense, he was.

Micha Wolfshtein, who collaborated closely with Akshai and paid
especial attention to the turbulence-modelling aspects.

Patankar's thesis of 1967 [Reference 7] made no mention of combustion; but
the numerical method which was described in it was subsequently
incorporated by the present author (approx 1969) into the GENMIX
computer code [Reference 8], in the
exemplification of which the combustion of methane with air played
an important part.

This computer code could simulate laminar and turbulent flame jets;
and it was later (1971) used for the prediction of laminar flame
propagation
[Reference 9]. However, it was not able to simulate combustion
phenomena in which "recirculation", ie reverse flow, played a
significant part; so something else had to be devised.

GENMIX will be made available for down-loading from CHAM's website,
if there is a demand.

The "something else" was the "stream-function-vorticity" method
(approx 1968)
which, after much travail, became for a few years the main means for
computing recirculating flows.

So far as the present author recalls, the main ingredients were:-

the ideas, to be found in textbooks on fluid mechanics, that:-

in two-dimensional steady (or uniform-density) flows, the velocity
field could be expressed in terms of the gradient of a scalar, the
stream-function;

the stream function could be deduced by solving a Laplace-type
differential equation, by well-established iterative means, of
which the source term on the right-hand side was the vorticity;

the vorticity, which varied from place to place, was in principle
amenable to computation by solution of a "transport equation", of
the same kind as governs concentration, temperature, kinetic energy
of turbulence (for, by this time "turbulence models" were coming
into prominence) and other properties;

the "home-grown" concept of "upwind differencing", which derived
from the author's childhood experience of having lived near a
pig-sty, and therefore known well how the direction of the wind
influenced the strength of the influence of near neighbours; and

the naive concept that it should be possible to devise an
iterative scheme which skipped cyclically:

from vorticity to stream function,

from stream function to velocity,

from velocity to turbulence quantitites,

from turbulence to effective viscosity,

from effective viscosity to vorticity transport,

and would indeed converge.

The computer programming and testing were carried out by Akshai
Runchal and Micha Wolfshtein; and the theory and results
(including the program) were published as a book in Reference 10
(1969).

Although Runchal and Wolfshtein had been concerned only with
non-reacting flows, the present author and WM Pun had been applying
the same methodology to flows with chemical reaction.

This work was
reported in a separate publication [Reference 11], perhaps the very
first (1968) publication in which CFD was applied to a recirculating flow
exhibiting combustion.
Click here for results.
The computer program was included as a final chapter of Reference 10.

Shortly afterwards it was used by British Coal Utilisation Research
Association (Morgan and Gibson, 1977)
as the basis of the first model of a coal-fired furnace.
The size distribution of the particles was one of the features calculated.

Once again it is necessary to remark that the physical modelling was
naive, and that the mathematical method (stream-function-vorticity)
ultimately proved not to be easily extensible to three
dimensions.
However, significant forward steps had been taken.

The Imperial College team was slow in deciding which was the best
way to handle three-dimensional problems, at first hoping that
stream-function-vorticity methods could be generalised. Reference
12 exemplifies this aspiration.

The best first step in the 3D direction was probably the SIVA
(SImultaneous Variable Adjustment) procedure about which a
publication [Reference 13] eventually emerged. This contained,
incidentally, an application to combustion.

It was however the same paper which explained how the "SIMPLE"
procedure,
hitherto used only for 3D boundary layers, could also be used for
re-circulating flows; and it was finally SIMPLE rather than SIVA
which was then preferred.

However, it is proper now to recognise that the first person to
devise a method for and publish a paper (1972) on CFD applied to a 3D
furnace, was Ingo Zuber, of Czechoslovakia [Reference 14]. His
achievement is all the more praiseworthy because, in the
circumstances of the country and the times, Zuber's access to
Western scientific literature, and his computer resources, were both
extremely limited.

Much more notice was taken of the publication which recorded the
techniques finally (or at least for a long time) adopted by the
Imperial College group), namely the 1974 publication of Patankar and
Spalding [Reference 15].

This employed:

a cartesian or cylindrical-polar grid,

the SIMPLE algorithm, in which the equations for velocity components
and other variables are solved sequentially rather than
simultaneously,

temperature- and pressure-dependent density and viscosity,

the k-epsilon turbulence model,

the six-flux radiation model, and

a kinetically-controlled "global" chemical reaction

This method was widely disseminated by the authors and their
colleagues at Imperial College; and it was extensively adopted by
others during the following years.

To bring to a close this review of the more remote past, the PhD
thesis of Amr Serag-Eldin [Reference 16] will be mentioned. His
work at Imperial College between 1973 and 1976 was
probably the first ever carried out specifically for testing whether
a CFD code was capable of predicting the performance of a
steady-flow combustor of gas-turbine type.

The thesis was exemplary in its thoroughness and honesty. Of especial
interest, in view of subsequent experiences, are the following
extracts from Amr's preface:

I first tested the model for cold flow and obtained favourable
results.
I then tested it for hot flows and otained generally disappointing
results.....
Hence I adopted a more sophisticated combustion model, which takes
into account the effect of concentration fluctuations....
The agreement ..... improved markedly, but was still disappointing
in the primary zone ....
Again, this was attributed to the combustion model, which ....
overlooks the effect of chemical kinetics.

Right at the start, therefore, of the researches devoted to testing
the validity of CFD-based prediction procedures for combustion,
questions arose about how the influences of concentration fluctuations
and chemical kinetics, and especially the interactions between them,
were to be introduced into the model.

These questions have remained
incompletely resolved until the present day!

The improved models referred to, which took account of fluctuations
but not (adequately) of chemical kinetics, were those of References
17 and 18 (1971) namely the "eddy-break-up" and "presumed-pdf" methods.

In somewhat modified forms, they are still (regrettably?) in
widespread use.

The foregoing review reveals that, by the mid-1970s,
CFD-for-combustion had become a reality.

Adequate means had been
discovered and published for solving the relevant equations; and only
more computer power would be needed to enable large and geometrically
complex problems to be solved.

Moreover, models of turbulence, chemistry and radiation had been devised
which, though far from perfect, were enabling predictions to be made,
on occasion, of a quality justifying hope that steadily conducted
research would soon make them very good.

Although it was to the gas turbine that most attention was given,
because of the financial support which could be then obtained from the
aerospace industry, attention also began to be paid to the
reciprocating engine, to power-station furnaces and to fire hazards.

Thus, the present author has found among his papers a 1969 proposal,
made at a meeting of the Institution of Mechanical Engineers in
London [Reference 19] for the application of CFD to the Diesel
engine; and Patankar and he presented a paper concerned with
applications to furnaces in 1972 [Reference 20].

Readers of the remainder of the present paper may well conclude that
the optimism of those early years has proved to be sadly falsified by
subsequent achievements.

2. The present

It could be reasonably argued that it was the needs of the combustion
engineers in the aero-space industry which brought the CFD-software
business into existence, the reason being that the complexity of
the combustion process left expensive experimentation as the only
alternative.

Certainly, some of the first computer codes sold by CHAM to UK and
US gas-turbine manufacturers were specifically for combustor
simulation; for the desigers of the other gas-turbine components, ie
the compressor and the turbine, already possessed computer-based
methods which they judged (perhaps unwisely) to be satisfactory.

Several of those combustor codes are still in existence and use,
having of course also been significantly further developed by their
users; and at least one of them entered the public domain by way
of the US Army, enabling competing CFD-code vendors to start
business; which they did with alacrity.

Maintaining and refining a special-purpose computer code is an
expensive and arduous business, which few organizations can afford.
It has therefore proved more cost-effective to create and maintain
a few general-purpose computer codes, which can be applied to
special-purpose problems.

This strategy was first exemplified by CHAM's PHOENICS code,
released in 1981, and Creare's FLUENT code released in 1983. Both
were capable of simulating either reacting or non-reacting flows.
Every few years since then, in one country or another, further
general-purpose codes with similar capabilities have made their
appearance.

As a consequence, almost all industrial companies using
CFD techniques, for designing and improving their equipment or
processes, nowadays buy or lease software from one of the
CFD-software vendors.

The numerical methods which are most commonly employed differ
little, in essence, from those of Reference 15. The major novelties
are:

body-fitted-coordinate grids are often employed;

unstructured grids (ie those in which cells may be arbitrarily
arranged and addressed) are preferred in some codes, avoided by
others;

some codes employ fine-grid-embedding techniques which can bring the
benefits sought from unstructured grids without their disadvantages;

there is a tendency to use more-simultaneous and less-sequential
solution procedures;

a few codes can exploit parallel-computer architectures, by use of
"domain decomposition";

"multi-grid" solution procedures are employed so as to accelerate
convergence;

the six-flux radiation model is replaced by one or other of the
more-accurate, but more-expensive, discrete-transfer [Reference 21]
or discrete-ordinates [Reference 22] methods.

The consequence of these developments, coupled with the immense
increase in the power of computer hardware, is that it is now
possible for CFD models to be set up which fit the geometrical
complexities of the equipment very well, yet still provide accurate
numerical solutions in an acceptable time.

Whether the numerically accurate solutions provide realistic
predictions of how the combustors will actually behave is, of
course, quite another matter; for realism depends on the physical
models which are employed and on the correctness of the material
properties which are supplied to them.

The advances on the numerical side of modelling have not,
unfortunately, been matched by corresponding successes on the
physical side. Nevertheless, there have been several developments,
of which the outcomes most in evidence currently are:

chemical-kinetics models of great complexity, both for hydrocarbon
combustion and for the reactions giving rise to oxides of nitrogen;

detailed improvements of turbulence models of the k-epsilon type;

modifications of the "eddy-break-up" model for predicting the
influence of the turbulence energy and scale on the time-average
reaction rates [Reference 23](1976);

modifications of the "presumed-pdf" approach for the representation
of the effects of concentration fluctuations on the rates of
production of particular chemical species, for example NOX and
"smoke" [Reference 24](1980);

methods of avoiding the arbitrariness of the "presumed-pdf" approach
by computing the pdfs (ie probability-density functions) from
more-rigorously-based "pdf-transport methods" [Reference 25](1982).

Much valuable work has been done; but, in the present author's
opinion, reservations must be expressed about each of the items
mentioned, as follows:

There is still no agreement about which "reduced-chemistry" model
represents the best compromise in respect of realism and
computational economy.

The improvements recommended by various authors differ, with the
result that none have been generally accepted.

The "eddy-break-up" model requires not to be improved, but replaced;
for it represents (as does the flamelet model) a turbulent reacting
mixture as the mingling of
just two distinct fluids; and two is too small a number to do
justice to reality.

The presumptions about pdf shape lack general validity, and are used
more "because one must use something" than for plausible reasons.

The pdf-transport method, although admirable in intention, has been
held back by its reliance on the computationally expensive Monte
Carlo method, for which reason it is little used in engineering
practice.

Despite the shortcomings just alluded to, the use of CFD for
combustion sumulation has become widely accepted as being a valuable
aid to the designers and operators of equipment, and to those who are
concerned with its environmental and safety impacts.

A short list of active application areas now follows, but without
references, because a balanced list would be too large:

The success of the CFD-for-combustion campaign could be called
complete if nowadays all designs of combustion-related equipment were
near-finalized by the use of CFD predictions, and experimental
verification were called for only at the end, to ensure that the
predictions had been near-enough correct.

This is NOT the situation at the present time, for any of the fields
of application; and, as the years go by, its attainability has
appeared less rather than more probable.

As computers have increased in power, and mathematical methods
improved in efficiency, it has become less and less justifiable to
blame the discrepancies between predictions and measurements on the
coarseness of the grid or the inability to procure complete
convergence.

The deficiencies of the underlying physical models
have become, as a consequence, increasingly obvious.

Deficiencies of this kind are much harder to remove than are those
of the numerical kind. Computer scientists abound who can improve
hardware and software; and mathematicians who can devise more
efficient algorithms are also not rare.

An advance in science, however, which is what CFD-for-combustion
now requires, depends on rare combinations of circumstance, namely:

someone must have the "bright idea", and sufficient leisure and
energy to develop it until he or she is reasonably confident that it
represents a worth-while advance;

that person must then communicate it to others, who can pass it on,
possibly with augmentation, but at least without attenuation;

the idea then has somehow to survive the self-preserving tendencies
of the current conventional wisdom, to which, if it is indeed of
value, it must to some extent be opposed;

in due course the idea has to reach someone who has the intellectual
power to appreciate its value and a resource-distribution capability
to enabling it to be tried out.

In what particular sector of combustion science are "bright ideas"
most needed? In the view of the present author it is that concerned
with turbulence-chemistry interactions. This opinion will be
further developed in part 3.3 of the present paper.

3. The future

The future of CFD-for-combustion will be influenced by general
developments in the way CFD will be used. It is thefore worth turning
for a moment from the particular to the general.

In the view of the present author, the most significant change that
will come about will be through the use of the Internet.

The reason is that there exist three deterrents to the wider use of
computer-simulation techniques, especially by small and medium-sized
enterprises; these are:

the cost of the software;

the cost of hardware of sufficient power to run many fine-grid
simulations; and

the scarcity and expense of personnel capable of using them.

However, techniques are already available, and are being continuously
improved, for enabling an engineer with a flow-simulation problem to
have it solved by:

setting up the geometry of the apparatus, with the aid of a
computer-aided-design package, on his or her personal computer;

transmitting this via Internet, to a remote CFD-service centre;

supplying such additional information about:

inflows,

outflows,

what is to be predicted, and

how much he or she is prepared to pay,

as complete the specification of the problem in question;

after some time, return to his/her PC, and there find and explore a
graphically-displayed simulation of the flow in question;

receive such additional information as has been requested about:

particular features of the simulation, for example combustion
efficiency or production rate of NOX,

advice concerning the probable error bounds,

what was the cost of the service;

down-load the whole or part of the files embodying the simulation
for further study.

In order to illustrate the CAD-to-CFD part of this, a 1997 example
will be shown during delivery of the lecture, wherein
a domestic gas
burner was simulated. This particular calculation was, as it
happens, not performed remotely; but it could have been.

The change that seems likely to come into being has been
characterised as like that in society when "bucket-and-well"
technology was replaced by "piped water".

When low-cost and quality-assured computations are available to all
"on-tap", and on payment-according-to-use terms, it seems likely that
many combustion engineers will choose that way of working.

The user of the remote computing service will not care on what
computational grid his or her combustor simulation has been
conducted; so he will be able to concentrate his attention only on
the physical results.

However, that freedom from worry lies a few years in the future;
therefore, until then, the CFD-code user will still need to concern
himself with what grid to use in order to fit his geometry.

It is widely believed that the only way to represent curved-wall
combustors, and such small but important features as fuel nozzles
and air-injection holes, is to use unstructured body-fitted
coordinate grids. However, since the creation of such grids is
often troublesome and expensive, it seems probable that better ways
will be sought and found.

Indeed, one such "better way" has been found quite recently.
It has been published on CHAM's website
[Reference 26]; and it seems probable that, unless something
even better
comes along, the techniques described there, namely
"PARSOL" and
"fine-grid embedding", will be widely used.

If so, body-fitted-coordinate grids will figure less often in the
combustor simulations of the future.

However, as has been emphasised above, easily-conducted simulations,
whether conducted remotely or at home, may be of little use (and even
dangerous, when too much trusted) if they are not based upon realistic
physical models.

It is therefore appropriate for the present author to disclose his
belief that the "multi-fluid model (MFM) of turbulent combustion"
[Reference 27] is likely to play a significant role in future
applications of CFD to combustion.

It is not possible to provide the justification for this belief in
the present paper; but, during the presentation of the lecture, some
material from two recent lectures will be shown.

The first
[Reference 28]
concerns the practicalities of using MFM for predicting smoke
generation in a gas-turbine combustor.

The second
[Reference 29]
is of a more scientific character. It shows how MFM comprehends a
wide range of combustion phenomena; and it provides a framework into
which "laminar-flamelet models" can be fitted, for those circumstances
in which they apply.

Some highlights from the paper in question will be shown during the
lecture.

4. Conclusions

The foregoing review, and the arguments presented in References 28
and 29, incline the present author to the following views:

Although the high hopes of the early years of CFD-for-combustion
have not yet been realised, the obstacles are being removed or
eroded significantly.

The power of computers, and especially those of parallel
architecture (which includes clusters of PCs), enables geometries
of realistic complexity to be simulated;

The development of Internet-based CFD services will make this power
available to everyone, on a convenient pay-by-use basis.

The use of body-fitted and unstructured grids will be increasingly
replaced by cartesian grids, enhanced by the "cut-cell" technique,
i.e. PARSOL.

It will thus be possible for engineers to export their CAD-geometry
files directly into the CFD code, whether this is on their
own computer or on the other side of the world.

The multi-fluid model of turbulence will make it possible to
investigate, with greater realism than has hitherto been possible,
how the main and secondary chemical reactions are influenced by
turbulence.